Do I have to refinance?

My separation agreement state "I shall assume and pay according to its terms and deed of trust secured by the formal marital residence…Neither party shall take any action to increase the amount of the mortgage or deed of trust obligation or extend the payments in any way. The deed is in my name but the mortgage is not. I can afford to make the payments. Can my ex force me to refinance when we go to finalize our divorce?

No, your agreement does not require you to refinance the loan, only to pay according to the terms of the existing mortgage.